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<br> <h1> Link to the source code for this example: </h1>
<a href="https://github.com/libMesh/libmesh/tree/master/examples/miscellaneous/miscellaneous_ex13" target="_blank">Open miscellaneous_ex13 in new tab.</a>
<a name="output"></a>
<br><br><br> <h1> The console output of the program: </h1>
<pre>
***************************************************************
* Running Example miscellaneous_ex13:
*   ./example-opt -pc_type jacobi -ksp_type cg
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=3
  n_nodes()=1329
    n_local_nodes()=1329
  n_elem()=416
    n_local_elem()=416
    n_active_elem()=416
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "Shell"
    Type "LinearImplicit"
    Variables={ "u" "v" "w" "theta_x" "theta_y" "theta_z" }
    Finite Element Types="LAGRANGE"
    Approximation Orders="SECOND"
    n_dofs()=7974
    n_local_dofs()=7974
    n_constrained_dofs()=486
    n_local_constrained_dofs()=486
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 89.7201
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 156
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 486
      Average DoF Constraint Length= 0
      Number of Node Constraints = 0

z-displacement of the point C: 164.322
Analytic solution: 164.24
y-displacement of the point D: 4.15289
Analytic solution: 4.114

 ------------------------------------------------------------------------------------------------
| Time:           Thu Nov 11 12:17:11 2021                                                       |
| OS:             Linux                                                                          |
| HostName:       thinkpad                                                                       |
| OS Release:     4.15.0-51-generic                                                              |
| OS Version:     #55-Ubuntu SMP Wed May 15 14:27:21 UTC 2019                                    |
| Machine:        x86_64                                                                         |
| Username:       jwpeterson                                                                     |
| Configuration:  /home/jwpeterson/software/libmesh-src/configure  'INSTALL=/usr/bin/install -C' |
|  '--enable-everything'                                                                         |
|  '--enable-slepc'                                                                              |
|  '--with-metis=PETSc'                                                                          |
|  '--with-subdomain-id-bytes=4'                                                                 |
|  '--with-boundary-id-bytes=4'                                                                  |
|  '--disable-glpk'                                                                              |
|  '--enable-unique-id'                                                                          |
|  '--with-unique-id-bytes=4'                                                                    |
|  '--enable-hdf5'                                                                               |
|  '--with-hdf5=/home/jwpeterson/software/libmesh_install/hdf5'                                  |
|  '--with-nlopt-include=/home/jwpeterson/software/libmesh_install/nlopt/include'                |
|  '--with-nlopt-lib=/home/jwpeterson/software/libmesh_install/nlopt/lib'                        |
|  '--with-capnproto=/home/jwpeterson/software/libmesh_install/capnp'                            |
|  '--disable-parmetis'                                                                          |
|  '--disable-ifem'                                                                              |
|  '--disable-gmv'                                                                               |
|  '--prefix=/home/jwpeterson/software/libmesh_install/opt_real/libmesh'                         |
|  '--with-methods=opt'                                                                          |
|  '--enable-shared'                                                                             |
|  '--enable-perflog'                                                                            |
|  '--disable-deprecated'                                                                        |
|  '--enable-nanoflann-pointlocator'                                                             |
|  '--enable-petsc-required'                                                                     |
|  'PETSC_DIR=/opt/petsc/3.15'                                                                   |
|  'SLEPC_DIR=/opt/slepc/3.15'                                                                   |
 ------------------------------------------------------------------------------------------------
 -----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=2.27938, Active time=2.27074                                                    |
 -----------------------------------------------------------------------------------------------------------------
| Event                              nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                               w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|-----------------------------------------------------------------------------------------------------------------|
|                                                                                                                 |
|                                                                                                                 |
| DefaultCoupling                                                                                                 |
|   operator()                       416        0.0003      0.000001    0.0003      0.000001    0.01     0.01     |
|                                                                                                                 |
| DofMap                                                                                                          |
|   add_neighbors_to_send_list()     1          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   build_constraint_matrix()        416        0.0008      0.000002    0.0008      0.000002    0.03     0.03     |
|   build_sparsity()                 1          0.0212      0.021246    0.0219      0.021924    0.94     0.97     |
|   cnstrn_elem_mat_vec()            416        0.0012      0.000003    0.0012      0.000003    0.05     0.05     |
|   create_dof_constraints()         1          0.0006      0.000598    0.0009      0.000922    0.03     0.04     |
|   distribute_dofs()                1          0.0001      0.000109    0.0004      0.000387    0.00     0.02     |
|   dof_indices()                    9606       0.0015      0.000000    0.0015      0.000000    0.07     0.07     |
|   prepare_send_list()              2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                         1          0.0003      0.000278    0.0003      0.000278    0.01     0.01     |
|                                                                                                                 |
| EquationSystems                                                                                                 |
|   build_parallel_solution_vector() 1          0.0010      0.001029    0.0014      0.001365    0.05     0.06     |
|   build_solution_vector()          1          0.0000      0.000009    0.0014      0.001374    0.00     0.06     |
|                                                                                                                 |
| ExodusII_IO                                                                                                     |
|   write_nodal_data()               1          0.0087      0.008708    0.0087      0.008708    0.38     0.38     |
|                                                                                                                 |
| FE                                                                                                              |
|   compute_shape_functions()        832        0.0004      0.000001    0.0004      0.000001    0.02     0.02     |
|   init_shape_functions()           832        0.0009      0.000001    0.0009      0.000001    0.04     0.04     |
|                                                                                                                 |
| FEMap                                                                                                           |
|   compute_map()                    832        0.0087      0.000010    0.0087      0.000010    0.38     0.38     |
|   init_reference_to_physical_map() 832        0.0019      0.000002    0.0019      0.000002    0.08     0.08     |
|   inverse_map()                    2          0.0000      0.000003    0.0000      0.000003    0.00     0.00     |
|                                                                                                                 |
| Mesh                                                                                                            |
|   find_neighbors()                 2          0.0004      0.000180    0.0004      0.000180    0.02     0.02     |
|   renumber_nodes_and_elem()        4          0.0000      0.000008    0.0000      0.000008    0.00     0.00     |
|   write()                          1          0.0001      0.000053    0.0008      0.000784    0.00     0.03     |
|                                                                                                                 |
| MeshBase                                                                                                        |
|   prepare_for_use()                2          0.0001      0.000045    0.0005      0.000247    0.00     0.02     |
|                                                                                                                 |
| MeshOutput                                                                                                      |
|   write_equation_systems()         1          0.0000      0.000012    0.0101      0.010094    0.00     0.44     |
|                                                                                                                 |
| NameBasedIO                                                                                                     |
|   read()                           1          0.0015      0.001534    0.0015      0.001534    0.07     0.07     |
|                                                                                                                 |
| Partitioner                                                                                                     |
|   set_node_processor_ids()         1          0.0001      0.000098    0.0001      0.000098    0.00     0.00     |
|   single_partition_range()         2          0.0000      0.000007    0.0000      0.000007    0.00     0.00     |
|                                                                                                                 |
| PetscLinearSolver                                                                                               |
|   solve()                          1          1.9924      1.992411    1.9924      1.992411    87.74    87.74    |
|                                                                                                                 |
| PointLocatorNanoflann                                                                                           |
|   init()                           2          0.0001      0.000049    0.0001      0.000049    0.00     0.00     |
|   operator()                       1          0.0000      0.000004    0.0000      0.000009    0.00     0.00     |
|                                                                                                                 |
| System                                                                                                          |
|   assemble()                       1          0.2270      0.227022    0.2417      0.241723    10.00    10.65    |
|                                                                                                                 |
| XdrIO                                                                                                           |
|   read()                           1          0.0006      0.000576    0.0007      0.000676    0.03     0.03     |
|   read_header()                    1          0.0000      0.000002    0.0000      0.000002    0.00     0.00     |
|   write()                          1          0.0007      0.000731    0.0007      0.000731    0.03     0.03     |
 -----------------------------------------------------------------------------------------------------------------
| Totals:                            14216      2.2707                                          100.00            |
 -----------------------------------------------------------------------------------------------------------------


***************************************************************
* Done Running Example miscellaneous_ex13:
*   ./example-opt -pc_type jacobi -ksp_type cg
***************************************************************
***************************************************************
* Running Example miscellaneous_ex13:
*   ./example-opt -distributed_load 1 -pc_type jacobi -ksp_type cg
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=3
  n_nodes()=1329
    n_local_nodes()=1329
  n_elem()=416
    n_local_elem()=416
    n_active_elem()=416
  n_subdomains()=1
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "Shell"
    Type "LinearImplicit"
    Variables={ "u" "v" "w" "theta_x" "theta_y" "theta_z" }
    Finite Element Types="LAGRANGE"
    Approximation Orders="SECOND"
    n_dofs()=7974
    n_local_dofs()=7974
    n_constrained_dofs()=486
    n_local_constrained_dofs()=486
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 89.7201
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 156
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 486
      Average DoF Constraint Length= 0
      Number of Node Constraints = 0


 ------------------------------------------------------------------------------------------------
| Time:           Thu Nov 11 12:17:11 2021                                                       |
| OS:             Linux                                                                          |
| HostName:       thinkpad                                                                       |
| OS Release:     4.15.0-51-generic                                                              |
| OS Version:     #55-Ubuntu SMP Wed May 15 14:27:21 UTC 2019                                    |
| Machine:        x86_64                                                                         |
| Username:       jwpeterson                                                                     |
| Configuration:  /home/jwpeterson/software/libmesh-src/configure  'INSTALL=/usr/bin/install -C' |
|  '--enable-everything'                                                                         |
|  '--enable-slepc'                                                                              |
|  '--with-metis=PETSc'                                                                          |
|  '--with-subdomain-id-bytes=4'                                                                 |
|  '--with-boundary-id-bytes=4'                                                                  |
|  '--disable-glpk'                                                                              |
|  '--enable-unique-id'                                                                          |
|  '--with-unique-id-bytes=4'                                                                    |
|  '--enable-hdf5'                                                                               |
|  '--with-hdf5=/home/jwpeterson/software/libmesh_install/hdf5'                                  |
|  '--with-nlopt-include=/home/jwpeterson/software/libmesh_install/nlopt/include'                |
|  '--with-nlopt-lib=/home/jwpeterson/software/libmesh_install/nlopt/lib'                        |
|  '--with-capnproto=/home/jwpeterson/software/libmesh_install/capnp'                            |
|  '--disable-parmetis'                                                                          |
|  '--disable-ifem'                                                                              |
|  '--disable-gmv'                                                                               |
|  '--prefix=/home/jwpeterson/software/libmesh_install/opt_real/libmesh'                         |
|  '--with-methods=opt'                                                                          |
|  '--enable-shared'                                                                             |
|  '--enable-perflog'                                                                            |
|  '--disable-deprecated'                                                                        |
|  '--enable-nanoflann-pointlocator'                                                             |
|  '--enable-petsc-required'                                                                     |
|  'PETSC_DIR=/opt/petsc/3.15'                                                                   |
|  'SLEPC_DIR=/opt/slepc/3.15'                                                                   |
 ------------------------------------------------------------------------------------------------
 -----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=2.25393, Active time=2.2456                                                     |
 -----------------------------------------------------------------------------------------------------------------
| Event                              nCalls     Total Time  Avg Time    Total Time  Avg Time    % of Active Time  |
|                                               w/o Sub     w/o Sub     With Sub    With Sub    w/o S    With S   |
|-----------------------------------------------------------------------------------------------------------------|
|                                                                                                                 |
|                                                                                                                 |
| DefaultCoupling                                                                                                 |
|   operator()                       416        0.0003      0.000001    0.0003      0.000001    0.01     0.01     |
|                                                                                                                 |
| DofMap                                                                                                          |
|   add_neighbors_to_send_list()     1          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   build_constraint_matrix()        416        0.0007      0.000002    0.0007      0.000002    0.03     0.03     |
|   build_sparsity()                 1          0.0216      0.021568    0.0222      0.022204    0.96     0.99     |
|   cnstrn_elem_mat_vec()            416        0.0012      0.000003    0.0012      0.000003    0.05     0.05     |
|   create_dof_constraints()         1          0.0006      0.000565    0.0008      0.000849    0.03     0.04     |
|   distribute_dofs()                1          0.0001      0.000106    0.0004      0.000377    0.00     0.02     |
|   dof_indices()                    9605       0.0013      0.000000    0.0013      0.000000    0.06     0.06     |
|   prepare_send_list()              2          0.0000      0.000000    0.0000      0.000000    0.00     0.00     |
|   reinit()                         1          0.0003      0.000271    0.0003      0.000271    0.01     0.01     |
|                                                                                                                 |
| EquationSystems                                                                                                 |
|   build_parallel_solution_vector() 1          0.0010      0.001006    0.0013      0.001325    0.04     0.06     |
|   build_solution_vector()          1          0.0000      0.000009    0.0013      0.001334    0.00     0.06     |
|                                                                                                                 |
| ExodusII_IO                                                                                                     |
|   write_nodal_data()               1          0.0084      0.008404    0.0084      0.008404    0.37     0.37     |
|                                                                                                                 |
| FE                                                                                                              |
|   compute_shape_functions()        832        0.0004      0.000001    0.0004      0.000001    0.02     0.02     |
|   init_shape_functions()           832        0.0008      0.000001    0.0008      0.000001    0.04     0.04     |
|                                                                                                                 |
| FEMap                                                                                                           |
|   compute_map()                    832        0.0084      0.000010    0.0084      0.000010    0.37     0.37     |
|   init_reference_to_physical_map() 832        0.0019      0.000002    0.0019      0.000002    0.08     0.08     |
|                                                                                                                 |
| Mesh                                                                                                            |
|   find_neighbors()                 2          0.0004      0.000175    0.0004      0.000175    0.02     0.02     |
|   renumber_nodes_and_elem()        4          0.0000      0.000007    0.0000      0.000007    0.00     0.00     |
|   write()                          1          0.0001      0.000051    0.0008      0.000755    0.00     0.03     |
|                                                                                                                 |
| MeshBase                                                                                                        |
|   prepare_for_use()                2          0.0001      0.000042    0.0005      0.000239    0.00     0.02     |
|                                                                                                                 |
| MeshOutput                                                                                                      |
|   write_equation_systems()         1          0.0000      0.000011    0.0097      0.009749    0.00     0.43     |
|                                                                                                                 |
| NameBasedIO                                                                                                     |
|   read()                           1          0.0015      0.001483    0.0015      0.001483    0.07     0.07     |
|                                                                                                                 |
| Partitioner                                                                                                     |
|   set_node_processor_ids()         1          0.0001      0.000099    0.0001      0.000099    0.00     0.00     |
|   single_partition_range()         2          0.0000      0.000007    0.0000      0.000007    0.00     0.00     |
|                                                                                                                 |
| PetscLinearSolver                                                                                               |
|   solve()                          1          1.9712      1.971171    1.9712      1.971171    87.78    87.78    |
|                                                                                                                 |
| System                                                                                                          |
|   assemble()                       1          0.2240      0.223999    0.2382      0.238242    9.98     10.61    |
|                                                                                                                 |
| XdrIO                                                                                                           |
|   read()                           1          0.0006      0.000556    0.0007      0.000657    0.02     0.03     |
|   read_header()                    1          0.0000      0.000002    0.0000      0.000002    0.00     0.00     |
|   write()                          1          0.0007      0.000704    0.0007      0.000704    0.03     0.03     |
 -----------------------------------------------------------------------------------------------------------------
| Totals:                            14210      2.2456                                          100.00            |
 -----------------------------------------------------------------------------------------------------------------


***************************************************************
* Done Running Example miscellaneous_ex13:
*   ./example-opt -distributed_load 1 -pc_type jacobi -ksp_type cg
***************************************************************
</pre>
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